Crystalline Structure of Accretion Disks: Features of the Global Model

Abstract: In this paper, we develop the analysis of a two-dimensional magnetohydrodynamical configuration for an axially symmetric and rotating plasma (embedded in a dipole like magnetic field), modeling the structure of a thin accretion disk around a compact astrophysical object. Our study investigates the global profile of the disk plasma, in order to fix the conditions for the existence of a crystalline morphology and ring sequence, as outlined by the local analysis pursued in [1, 2]. In the linear regime, when the electromagnetic back-reaction of the plasma is small enough, we show the existence of an oscillating radial behavior for the flux surface function which very closely resembles the one outlined in the local model, apart from a radial modulation of the amplitude. In the opposite limit, corresponding to a dominant back-reaction in the magnetic structure over the field of central object, we can recognize the existence of a ring-like decomposition of the disk, according to the same modulation of the magnetic flux surface, and a smoother radial decay of the disk density, with respect to the linear case. In this extreme non-linear regime, the global model seems to predict a configuration very close to that of the local analysis, but here the thermostatic pressure, crucial for the equilibrium setting, is also radially modulated. Among the conditions requested for the validity of such a global model, the confinement of the radial coordinate within a given value sensitive to the disk temperature and to the mass of the central objet, stands; however, this condition corresponds to dealing with a thin disk configuration.